Problem: Simplify the following expression: $ q = \dfrac{-9z - 3}{-5} + \dfrac{10}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-9z - 3}{-5} \times \dfrac{7}{7} = \dfrac{-63z - 21}{-35} $ Multiply the second expression by $\dfrac{-5}{-5}$ $ \dfrac{10}{7} \times \dfrac{-5}{-5} = \dfrac{-50}{-35} $ Therefore $ q = \dfrac{-63z - 21}{-35} + \dfrac{-50}{-35} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-63z - 21 - 50}{-35} $ $q = \dfrac{-63z - 71}{-35}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{63z + 71}{35}$